Celebratio Mathematica — Ranicki

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Works connected to Aidan H. Schofield

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A. Neeman, A. Ranicki, and A. Schofield: “Representations of algebras as universal localizations,” Math. Proc. Camb. Philos. Soc. 136 : 1 (2004), pp. 105–117. MR 2034017 Zbl 1088.16020 ArXiv math/0205034 article

Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra \( S \) in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adjoin inverses to some of the arrows in the quiver, we show that the path algebra of the new quiver with relations is \( M_n(S) \) where \( n \) is the number of vertices in our quiver. The slogan would be that every finitely presented algebra is Morita equivalent to a universal localization of a finite dimensional algebra.

Aidan H. Schofield	Related
Amnon Neeman	Related

D. Sheiham: “Universal localization of triangular matrix rings,” Proc. Am. Math. Soc. 134 : 12 (2006), pp. 3465–3474. Prepared posthumously by Andrew Ranicki and Aidan Schofield. MR 2240657 Zbl 1115.16010 article

Desmond Sheiham	Related
Aidan H. Schofield	Related